A spring is attached to a block, mass m, on a frictionless ramp. Let be the angle the plane makes with the horizontal. Assume the spring has unstreched length t and constant k.
1) establish the forces acting on the block. I got normal reation, weight and the restoring force.
2) Find L,the length the spring streches to hold the block in equlibrium. I got so by hooke's law but the answer said I needed to add t. Can anyone explain why?
3)show the mechanincal energy of the block is given by . Where x=the displacement measured up the slopeand chosen such that x=0 when l=t
I know that E=PE +KE but don't know how to obtain the equation.
Thanks
Thanks though I am having a bit of trouble with the signs. If we take up the slope as positive, then we have stored energy= , loss of and KE=1/2(mv^2). Is that correct?
The next question is what is the total mechanical energy when the spring is pushed up a distance y from the unstreched length. My answer is , again taking up the slope as the positive direction.
Then it asks when the cart is released from rest at position y, what is its speed when the spring has returned to its unstretched length t? Initally and finally . Equating the two yields v= .
Am I correct. Again thanks
is a constant that you do not want to depend on your reference frame. The minute you say you have partially specified a reference frame. In fact we do not have a reference fame of this sort here we just have a single coordinate for displacement which is positive up the incline.
We need the change in PE for a displacement up the incline to be positive so if we have an unsigned g the change in PE is . If we use a negative signed we will have the change in PE as , but now we have to worry about the orientation of the coordinates in a 2 or 3D space containing our inclined plane.
In fact it is usual to define g unsigned (see the Wikipedia page on standard gravity for an example)
CB